The former Red Devils goalscorer has led United’s revitalisation since returning to Old Trafford.
Manchester United have won 10 of 11 games across all competitions since his appointment on an interim basis.
The team’s incredible form under his guidance has led to calls for the 45-year-old to get the job permanently.
Victories away at Tottenham and Arsenal in the Premier League and FA Cup respectively have been Solskjaer’s most impressive scalps to date.
But the fixture list has been largely kind, and fourth-placed United now have tough successive tests against PSG, Chelsea and Liverpool.
Attention on the Premier League loses focus until United return to action at home to their arch-rivals on February 24.
Before then, Ligue 1 champions PSG visit tomorrow (8pm) for their Champions League round of 16 first leg.
United then travel down to London next Monday (7.30pm) in a bid to clinch an FA Cup quarter-final place at Chelsea.
“All he has to do is continue in the same vein”
Solskjaer’s dominating, attacking football – reminiscent of United’s style and approach under Sir Alex Ferguson – has won him many fans and plaudits.
So even if PSG and Chelsea prove too big a hurdle for Solskjaer’s ever-improving United to overcome just yet, Neville feels it should not deny him the managerial role full time.
Discussing Solskjaer getting the job permanently, Neville said on the Gary Neville podcast: “All he has to do is continue in the same vein.
“The way in which they go out, if they were to lose to PSG or at Stamford Bridge, as long as the nature of the performances and the feeling continues.
“If they were out of those competitions, I still don’t think it’s a case of Ole shouldn’t get the job because they lost to PSG or Chelsea, I think it’s more about the nature and continuing to grow.
“If the performances are still good, I think it will be very difficult for the board not to give him the job.
“Because the reality is it’s too big a risk to be sat here next October, November, having put a new manager in charge, if the manager in charge now is delivering title winning results.”
With Chelsea and Liverpool still to come in February, injury-plagued PSG pose the first threat to United’s unbeaten streak since Solskjaer’s arrival when they visit Old Trafford tomorrow night.